Does Node.js and Ruby on Plesk support WebSockets (socket.io)?
How to provide WebSockets feature to customers?
Plesk itself does not forbid to use WebSockets, it only provides runtime environment to run Node.js and Ruby using Phusion Passenger, or iisnode.
The rest depends on particular website code design/implementation details.
The sample "Phusion Passenger: Node.js WebSocket demo" application can be used to verify whether WebSocket connections are working fine on the webserver: https://github.com/phusion/passenger-nodejs-websocket-demo